Show commands:
SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 55488.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55488.ca1 | 55488cv2 | \([0, -1, 0, -68589, 6940731]\) | \(-23100424192/14739\) | \(-22768872287424\) | \([]\) | \(248832\) | \(1.5040\) | |
| 55488.ca2 | 55488cv1 | \([0, -1, 0, 771, 39411]\) | \(32768/459\) | \(-709065226944\) | \([]\) | \(82944\) | \(0.95465\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 55488.ca have rank \(0\).
Complex multiplication
The elliptic curves in class 55488.ca do not have complex multiplication.Modular form 55488.2.a.ca
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
